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arXiv · 2501.18053

Varieties of prime tropical ideals and the dimension of the coordinate semiring

Dániel Joó·Kalina Mincheva
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Abstract

In this note we study the relationship between ideals and congruences of the tropical polynomial and Laurent polynomial semirings. We show that the variety of a non-zero prime ideal of the tropical (Laurent) polynomial semiring consists of at most one point. We also prove a result relating the dimension of an affine tropical variety and the dimension of its coordinate semiring.

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Dániel Joó, Kalina Mincheva. 2025-01-29. Varieties of prime tropical ideals and the dimension of the coordinate semiring. https://arxiv.org/abs/2501.18053

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